{"id":51907,"date":"2024-04-12T13:14:14","date_gmt":"2024-04-12T07:44:14","guid":{"rendered":"https:\/\/e-gmat.com\/blogs\/?p=51907"},"modified":"2024-04-12T13:14:15","modified_gmt":"2024-04-12T07:44:15","slug":"three-effective-strategies-for-drawing-inferences-in-difficult-tpa-questions","status":"publish","type":"post","link":"https:\/\/e-gmat.com\/blogs\/three-effective-strategies-for-drawing-inferences-in-difficult-tpa-questions\/","title":{"rendered":"Three Effective Strategies for Drawing Inferences in Difficult TPA Questions"},"content":{"rendered":"<span class=\"rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">A <\/span> <span class=\"rt-time\">4<\/span> <span class=\"rt-label rt-postfix\">min read <\/span><\/span>\n<h2 id=\"h-introduction\">Introduction<\/h2>\n\n\n\n<p>Many a times, while solving Difficult TPA questions, you reach a point where you feel that you do not sufficient information to carry forward or you feel that solving the question will take too long.\u00a0 Whenever you feel this way, always know that there is an inference waiting to be drawn.<\/p>\n\n\n\n<p>Let\u2019s see some examples of inferences that we can draw using Number Properties.<\/p>\n\n\n<div class=\"ub-buttons align-button-center\"  id=\"ub-button-f0a9accc-d97a-47df-9a85-720e950381ee\"><div class=\"ub-button-container\">\n    <a href=\"https:\/\/resources.e-gmat.com\/sign-up-GFE-free-trial\" target=\"_blank\" rel=\"noopener noreferrer external\" class=\"ub-button-block-main ub-button-medium ub-button-flex-medium\" role=\"button\" data-wpel-link=\"external\">\n    <div class=\"ub-button-content-holder\"><span class=\"ub-button-icon-holder\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\"height=\"30\", width=\"30\"viewBox=\"0, 0, 512, 512\"><path fill=\"currentColor\" d=\"M256 0C114.6 0 0 114.6 0 256c0 141.4 114.6 256 256 256s256-114.6 256-256C512 114.6 397.4 0 256 0zM406.6 278.6l-103.1 103.1c-12.5 12.5-32.75 12.5-45.25 0s-12.5-32.75 0-45.25L306.8 288H128C110.3 288 96 273.7 96 256s14.31-32 32-32h178.8l-49.38-49.38c-12.5-12.5-12.5-32.75 0-45.25s32.75-12.5 45.25 0l103.1 103.1C414.6 241.3 416 251.1 416 256C416 260.9 414.6 270.7 406.6 278.6z\"><\/svg><\/span><span class=\"ub-button-block-btn\">Start GMAT Focus Preparation<\/span>\n    <\/div><\/a><\/div><\/div>\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n\n\n\n<h2 id=\"h-tpa_032\">TPA_032<\/h2>\n\n\n\n<h3 id=\"h-question\">Question<\/h3>\n\n\n\n<p>This is an official question (not from any of the mocks).&nbsp; Try your hand at it!<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" width=\"1024\" height=\"544\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture1-2-1024x544.png\" alt=\"\" class=\"wp-image-51908\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture1-2-1024x544.png 1024w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture1-2-300x159.png 300w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture1-2-768x408.png 768w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture1-2-1080x574.png 1080w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture1-2-400x212.png 400w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture1-2.png 1092w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<h3 id=\"h-inference\">Inference<\/h3>\n\n\n\n<p>Now let\u2019s observe how we solved it real quick by drawing inference:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" width=\"1024\" height=\"90\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture2-1-1024x90.png\" alt=\"\" class=\"wp-image-51909\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture2-1-1024x90.png 1024w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture2-1-300x26.png 300w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture2-1-768x68.png 768w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture2-1-1080x95.png 1080w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture2-1-400x35.png 400w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture2-1.png 1092w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>Here is the output of our translation of the dataset:<\/p>\n\n\n\n<ul><li>Earlier = Sales: Tech = 60:100 = 3:5<\/li><li>Now = Sales is 12 and Tech is 15<\/li><\/ul>\n\n\n\n<p>And here is the crucial inference that needs to be drawn at this point of the solution:<\/p>\n\n\n\n<ul><li># sales earlier = a multiple of 3 less than 12<\/li><\/ul>\n\n\n\n<p>And<\/p>\n\n\n\n<ul><li>&nbsp;# tech earlier = a multiple of 5 less than 15<\/li><\/ul>\n\n\n\n<p>And from this point onwards, we can work out the possible combinations from the choices to arrive at the final answer.&nbsp;<\/p>\n\n\n\n<p>You may watch the solution from 4:30 mark.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/wc5MeM_3gqI?rel=0\"\ntitle=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer rel=0; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"\"><\/iframe>\n\n\n\n<p><\/p>\n\n\n\n<h3 id=\"h-summary\">Summary<\/h3>\n\n\n\n<p>We infered that the quantities were multiples of specific numbers using the information about the ratio information given in the dataset.\u00a0 And this paved way further into the solution.\u00a0This is one of the examples of Difficult <a href=\"https:\/\/e-gmat.com\/blogs\/mastering-probability-in-tpa-questions-a-comprehensive-guide\/\" target=\"_blank\" rel=\"noreferrer noopener\" data-wpel-link=\"internal\">TPA Questions<\/a>. Now, let&#8217;s move further.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n\n\n\n<h2 id=\"h-tpa_056\">TPA_056<\/h2>\n\n\n\n<h3 id=\"h-question-1\">Question<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" width=\"1024\" height=\"530\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture3-3-1024x530.png\" alt=\"\" class=\"wp-image-51910\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture3-3-1024x530.png 1024w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture3-3-300x155.png 300w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture3-3-768x397.png 768w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture3-3-1080x559.png 1080w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture3-3-400x207.png 400w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture3-3.png 1092w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<h3 id=\"h-inference-1\">Inference<\/h3>\n\n\n\n<p>Upon simplifying, we arrive at this equation:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" width=\"553\" height=\"96\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture4-2.png\" alt=\"\" class=\"wp-image-51911\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture4-2.png 553w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture4-2-300x52.png 300w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture4-2-400x69.png 400w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/figure>\n\n\n\n<p>To solve this question, we use number properties, specifically related to product of two numbers.&nbsp; Observe how we have take common and arrive at product of an even and an odd number.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" width=\"421\" height=\"175\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture5-2.png\" alt=\"\" class=\"wp-image-51912\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture5-2.png 421w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture5-2-300x125.png 300w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture5-2-400x166.png 400w\" sizes=\"(max-width: 421px) 100vw, 421px\" \/><\/figure>\n\n\n\n<p>And then by comparing the two sides, we infer as shown and find the value of M as 3.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" width=\"161\" height=\"143\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture6-2.png\" alt=\"\" class=\"wp-image-51913\"\/><\/figure>\n\n\n\n<p>And likewise, we infer and arrive at the value of N as 6.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" width=\"196\" height=\"276\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture7-2.png\" alt=\"\" class=\"wp-image-51914\"\/><\/figure>\n\n\n\n<p>You may watch the detailed video solution here at 7:36 mark or to watch an alternate solution using the choices, watch from 5:30 mark.\u00a0 <\/p>\n\n\n\n<p><\/p>\n\n\n\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/vuZWoL_8Avc?rel=0\"\ntitle=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer rel=0; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"\"><\/iframe>\n\n\n\n<p><\/p>\n\n\n\n<h3 id=\"h-summary\">Summary<\/h3>\n\n\n\n<p>In this question, with a single equation with two variables, we converted expression of the sum into product of two numbers and we drew inferences from that product and arrived at the exact values of the two variables. This is another example of Difficult <a href=\"https:\/\/e-gmat.com\/blogs\/mastering-probability-in-tpa-questions-a-comprehensive-guide\/\" target=\"_blank\" rel=\"noreferrer noopener\" data-wpel-link=\"internal\">TPA Questions<\/a>. Let&#8217;s see the final one.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n\n\n\n<h2 id=\"h-tpa_069\">TPA_069<\/h2>\n\n\n\n<h3 id=\"h-question-2\">Question<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" width=\"1024\" height=\"568\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture8-2-1024x568.png\" alt=\"\" class=\"wp-image-51916\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture8-2-1024x568.png 1024w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture8-2-300x166.png 300w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture8-2-768x426.png 768w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture8-2-1080x599.png 1080w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture8-2-400x222.png 400w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture8-2.png 1092w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<h3 id=\"h-inference-2\">Inference<\/h3>\n\n\n\n<p>Per the scenario explained in this dataset, processes are repeating at regular intervals based on frequencies specific to each process as shown below:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" width=\"574\" height=\"180\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture9-2.png\" alt=\"\" class=\"wp-image-51917\" srcset=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture9-2.png 574w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture9-2-300x94.png 300w, https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/Picture9-2-400x125.png 400w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/figure>\n\n\n\n<p>Whenever you see such repetition, it should automatically infer that LCM is the concept at play.\u00a0 So, to solve this question, this is the crucial inference that you needed to draw.\u00a0 Watch this video at 7:24 to see why this is the case and get a complete clarity on this inference.\u00a0<\/p>\n\n\n\n<p><\/p>\n\n\n\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/XRJK-gwRNfk?rel=0\"\ntitle=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer rel=0; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"\"><\/iframe>\n\n\n\n<p><\/p>\n\n\n\n<h3 id=\"h-summary-1\">Summary<\/h3>\n\n\n\n<p>In this question, once we understood the scenario about repetition of tasks at fixed frequencies, we could infer that this question will require concept of LCM. Hence, we three strategues to solve Difficult <a href=\"https:\/\/e-gmat.com\/blogs\/mastering-probability-in-tpa-questions-a-comprehensive-guide\/\" target=\"_blank\" rel=\"noreferrer noopener\" data-wpel-link=\"internal\">TPA Questions<\/a>.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<h2 id=\"h-takeaway\">Takeaway<\/h2>\n\n\n\n<p>While solving TPA questions, when you feel that you are at a point where you cannot go any further, trust your knowledge and identify scope of drawing such inferences.\u00a0 Think of these inferences as the bridge between the point where you get stuck to the next step in your solution.\u00a0<\/p>\n\n\n\n<blockquote class=\"wp-block-quote\"><p>Inferences = Bridges!<\/p><\/blockquote>\n\n\n<div class=\"ub-styled-box ub-bordered-box\" id=\"ub-styled-box-be2a603e-877a-4c55-8432-ef5a04095eaf\">\n\n\n<p><span style=\"font-size: revert;\">Ready to tackle the GMAT Focus Edition? e-GMAT offers a <\/span><a style=\"font-size: revert;\" href=\"https:\/\/success.e-gmat.com\/new_study-plan\" data-wpel-link=\"external\" target=\"_blank\" rel=\"external noopener noreferrer\">Personalized Study Planner<\/a><span style=\"font-size: revert;\"> and top-notch <\/span><a style=\"font-size: revert;\" href=\"https:\/\/resources.e-gmat.com\/take-sigma-x-mock\" data-wpel-link=\"external\" target=\"_blank\" rel=\"external noopener noreferrer\">Free GFE mock exam<\/a><span style=\"font-size: revert;\"> to help you prepare effectively. 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Let\u2019s see some [&hellip;]<\/p>\n","protected":false},"author":74405,"featured_media":51920,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"off","_et_pb_old_content":"","_et_gb_content_width":"","ub_ctt_via":""},"categories":[11722,11726,92,94],"tags":[],"featured_image_src":"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2024\/04\/SME-Article.jpg","author_info":{"display_name":"Payal Tandon","author_link":"https:\/\/e-gmat.com\/blogs\/author\/payale-gmat-com\/"},"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.1.1 (Yoast SEO v17.1) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Three Effective Strategies for Drawing Inferences in Difficult TPA Questions<\/title>\n<meta name=\"description\" content=\"Master Difficult TPA Questions using key inferences from examples, helping bridge gaps in your problem-solving approach.\" \/>\n<meta name=\"robots\" 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